Volume units go up and down by the cube of the length factor, and capacity links to volume through one fact: 1 litre = 1000 cm³. Get those two ideas clear and most unit marks become safe.
This lesson follows work with a cylinder and a cone, because answers there often need turning into litres. It belongs to volume and capacity.
What are the key facts?
| Fact | Why |
|---|---|
| 1 cm³ = 1 millilitre (mL) | Definition used in measurement |
| 1 litre = 1000 mL = 1000 cm³ | A 10 cm cube |
| 1 m³ = 1000 litres | 1 000 000 cm³ ÷ 1000 |
| 1 m³ = 1 000 000 cm³ | 100 × 100 × 100 |
| 1 cm³ = 1000 mm³ | 10 × 10 × 10 |
How to convert
- Write the length factor, for example 1 m = 100 cm.
- Cube it. 100³ = 1 000 000.
- Multiply to go to the smaller unit (m³ to cm³), or divide to go to the larger unit.
- For capacity, change to cm³ first, then divide by 1000 for litres.
Worked example
A rectangular tank is 80 cm long, 50 cm wide and 40 cm high. How many litres of water does it hold when full?
Step 1, volume: 80 × 50 × 40 = 4000 × 40 = 160 000 cm³.
Step 2, to litres: 160 000 ÷ 1000 = 160 litres.
Now convert the same volume to m³. Since 1 m³ = 1 000 000 cm³, 160 000 ÷ 1 000 000 = 0.16 m³. Check: 0.16 m³ × 1000 = 160 litres, which agrees.
The mistake to watch for
The usual slip is to convert the volume with the length factor, once only.
Mistaken working: 2.4 m³ = 2.4 × 100 = 240 cm³
This treats the volume as a length.
The correction is to cube the factor: 2.4 × 1 000 000 = 2 400 000 cm³. A quick sense check helps: a cm³ is tiny, about the size of a sugar cube, so a cubic metre must contain a very large number of them.
Check yourself
1. Write 3.5 litres in cm³.
Show answer
3.5 × 1000 = 3500 cm³.
2. A skip has volume 0.75 m³. How many litres is that?
Show answer
1 m³ = 1000 litres, so 0.75 × 1000 = 750 litres.
3. A cuboid container measures 25 cm by 20 cm by 12 cm. How many litres can it hold?
Show answer
Volume = 25 × 20 × 12 = 500 × 12 = 6000 cm³. Then 6000 ÷ 1000 = 6 litres.
4. Convert 4500 mm³ to cm³.
Show answer
1 cm³ = 1000 mm³, so 4500 ÷ 1000 = 4.5 cm³.
Where this leads next
With units under control, move on to solving a reverse-dimension volume problem, where you start from a capacity and must work back to a length. The percentage-base explorer trains a similar habit: write down what you are starting from before you calculate.
Unit errors are easy to make and hard to spot in your own work. In online one-to-one Mathematics tuition, a teacher can watch your working and point out exactly where a factor went missing.